题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071321-43162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071321-24806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071322-66651.png)
小题1:填空:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071322-60573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071322-31867.png)
小题2:若线段BC的垂直平分线EF交BC于点E,交
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071321-24806.png)
小题3:探究:在抛物线的对称轴上是否存在点P,使⊙P与
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071321-24806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071323-87303.png)
答案
小题1:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071323-39948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071323-15177.png)
小题2:由(1)得抛物线的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071323-24677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071323-15974.png)
∴C(2,4)。
∵E为BC的中点,由中点坐标公式求得E的坐标为(3.5,2),……………………………..3分
设直线BC的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071324-52737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071324-70886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071324-30376.png)
∴直线BC的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071324-45434.png)
设直线EF的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071325-46818.png)
∵EF为BC的中垂线,∴EF⊥BC。∴由相似可得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071325-32165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071325-84009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071325-57460.jpg)
把E(3.5,2)代入得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071326-53228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071326-27532.png)
∴直线EF的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071326-53892.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071326-53892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071326-80400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071327-13352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071327-84311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071327-40540.png)
∴FC=FB=5-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071327-57785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-29093.png)
小题3:存在。作∠OBC的平分线交DC于点P,则P满足条件。
设P(2,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-80412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-17718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-80412.png)
∵点C的坐标是(2,4),点B的坐标是(5,0),
∴CD=4,DB=5-2=3。∴BC=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-67446.png)
∴sin∠BCD=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071329-59692.png)
当点P在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-17718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071329-50881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071329-82252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071329-26344.png)
当点P在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071328-17718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-11454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-14120.png)
∴在抛物线的对称轴上存在点P,使⊙P与x轴、直线BC都相切,
点P的坐标是(2,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071329-26344.png)
解析
(2)求出C(2,4)求得E的坐标为(3.5,2)和直线BC的表达式为y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-13648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-41402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-19298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071331-28326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071330-19298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071331-28326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071331-47376.png)
(3)作∠OBC的平分线交DC于点P,设P(2,a),根据抛物线解析式求出顶点C的坐标与点B的坐标,然后利用∠BCD的正弦列式即可求解
核心考点
试题【如图23,已知抛物线与轴相交于A、B两点,其对称轴为直线,且与x轴交于点D,AO=1.小题1:填空:=_______。=_______,点B的坐标为(_____】;主要考察你对二次函数定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071314-43469.png)
小题1:求证:不论m为何值,该二次函数图象的顶点P都在函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071315-12350.png)
小题2:若顶点P的横、纵坐标相等,求P点坐标
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071311-43676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071311-53667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071312-23676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071311-53667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071312-19691.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071258-58322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071259-85189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071259-85189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071259-83919.png)
小题1:求点A、B的坐标;
小题2:在抛物线的对称轴上找一点D,使|DC-DB|的值最大,求点D的坐标;
小题3:过点P作PQ∥y轴与抛物线交于点Q,连接QM,当四边形PQMN满足有一组对边相等时,求P点坐标.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071250-56991.png)
小题1:求BC边所在直线的解析式;
小题2:设点F为直线BC与y轴的交点,求经过点B,D,F的抛物线解析式;
小题3:判断▱ABCD的对角线的交点G是否在(2)中的抛物线上,并说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071244-72509.png)
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